Intrinsic violation of the Wiedemann-Franz law in interacting systems

TL;DR

This paper reveals a fundamental thermodynamic mechanism causing violations of the Wiedemann-Franz law in interacting systems, highlighting the role of temperature-dependent band structure renormalization in decoupling heat and charge transport.

Contribution

It introduces a thermodynamic explanation for WF law violations via energy drift from interactions, extending understanding of thermal transport in topological phases.

Findings

Thermal and electrical conductivities can decouple due to energy drift.

The Lorenz ratio deviation relates to thermoelectric response.

The framework helps distinguish topological robustness from Fermi liquid instabilities.

Abstract

The Wiedemann-Franz (WF) law dictates a universal ratio between thermal and electrical conductivities, is widely obeyed by Fermi liquid systems. Here, we identify a fundamental yet often overlooked, thermodynamic mechanism for the violation of WF law: the temperature-dependent renormalization of the electronic band structure. We demonstrate that the interaction-induced energy drift $\partial\epsilon_k/\partial T$, acts as an effective driving force that fundamentally decouples heat transport from charge transport. We derive a generalized transport relation linking the Lorenz ratio deviation directly to the thermoelectric response. Our findings provide a unified framework for understanding thermal transport in interacting topological phases and suggest the Lorenz ratio as a probe for distinguishing topological robustness from Fermi liquid instabilities.